Standard Model Advances with Irreducible Two-Particle States and Electromagnetic Interaction Correlation

The fundamental building blocks of particle physics and the forces governing them remain a central question for physicists worldwide. Walter Smilga, based in Munich, alongside colleagues, now propose a novel approach to understanding these interactions by examining irreducible representations of the Poincaré group. Their research demonstrates that two-particle states possess a structure mirroring the electromagnetic interaction, complete with a coupling constant matching the experimentally observed value. This work is significant because it suggests the Standard Model’s reliance on manually inserted coupling constants may stem from an incomplete understanding of the underlying mathematical structure. Furthermore, the team extends this framework to gravity, predicting a galaxy-specific gravitational constant that aligns with current experimental data, potentially offering a path towards a more complete and consistent theory of fundamental forces.

Walter Smilga, based in Munich, alongside colleagues, now propose a novel approach to understanding these interactions by examining irreducible representations of the Poincaré group. Their research demonstrates that two-particle states possess a structure mirroring the electromagnetic interaction, complete with a coupling constant matching the experimentally observed value. This work is significant because it suggests the Standard Model’s reliance on manually inserted coupling constants may stem from an incomplete understanding of the underlying mathematical structure.

Furthermore, the team extends this framework to gravity, predicting a galaxy-specific gravitational constant that aligns with current experimental data, potentially offering a path towards a more complete and consistent theory of fundamental forces. Research focuses on product states and their correlation with the structure of the electromagnetic interaction, identifying a coupling constant numerically equivalent to the electromagnetic coupling constant itself. This constant functions as a normalisation factor for these two-particle states, a concept central to the investigation. The Standard Model currently addresses the electromagnetic interaction through a perturbative algorithm, relying on the manual insertion of the experimentally determined electromagnetic coupling constant.

However, researchers argue that introducing a normalisation factor necessitates a thorough examination of the integral’s range of integration, with potential adjustments required to ensure accuracy. This work challenges the conventional approach by advocating for a self-consistent determination of this fundamental constant.

Stern-Gerlach, Poincaré Symmetry and Relativistic Quantum States The

This lengthy text presents a highly theoretical exploration of the foundations of relativistic quantum mechanics, its connection to gravity, and the surprisingly central role of the Stern-Gerlach experiment. The author argues for a consistent framework built upon the principles of Poincaré symmetry and irreducible representations of particle states. The Stern-Gerlach experiment is positioned not just as a demonstration of spin quantization, but as a foundational element for understanding the resolution of conflict between discrete and continuous degrees of freedom in quantum mechanics.

Scientists have demonstrated a profound connection between the mathematical structure of the Stern-Gerlach experiment and the properties of a spin-1/2 particle, revealing its equivalence to an irreducible unitary representation of the Poincaré group. Their work details how two-particle states are formed through an integral over product states, describing a correlation between particles mirroring the electromagnetic interaction. Crucially, the team discovered that the coupling constant governing this interaction numerically equals the established electromagnetic coupling constant, functioning as the normalisation factor for these two-particle states. Experiments revealed that the calculated value of this normalisation factor is inextricably linked to the domain of integration defining the two-particle states.

Researchers argue that inserting the electromagnetic coupling constant into the Standard Model’s perturbation algorithm without verifying this integration range introduces an inconsistency. Adjusting the integration domain delivers a mathematically consistent structure for a non-local, relativistic, two-particle mechanics, effectively refining the perturbation algorithm. This adjustment provides a framework grounded in the principles of relativistic quantum mechanics, offering a novel approach to understanding fundamental interactions. Further investigation into multi-particle representations has led to the prediction of a gravitational interaction, which, in the quasi-classical limit, aligns with the field equations of conformal gravity.

A galaxy-specific calculation of the gravitational constant yielded a value matching the experimentally determined constant, confirming the theoretical framework’s predictive power. The study establishes that a particle’s behaviour in spacetime is fundamentally the evolution of information, extending this concept to two- and multi-particle configurations through tensor products of state spaces. Classification of these configurations by mass and angular momentum reveals a spectrum of irreducible representations with distinct energetic properties, manifesting as interactions between particles. The team’s analysis of a two-particle scattering experiment resulted in a scattering amplitude determined by the constant 4πω2, calculated to be 1/137.036.

This value precisely coincides with the experimental value of the electromagnetic fine-structure constant, 1/137.035999, demonstrating that the formation of a two-particle eigenstate generates an interaction characteristic of electromagnetism. Moreover, the research highlights a discrepancy within the Standard Model, where the fine-structure constant is inserted manually, without consideration of the integration domain, and proposes replacing the standard four-dimensional momentum space with the calculated domain Ω to regularise divergent integrals while preserving Poincaré invariance. Extending this approach to configurations of N spinless particles, estimated at 2.4x 1067, the approximate number of atoms in our galaxy, further solidifies the theoretical framework.

Poincaré Group Links Spin and Electromagnetism

The analysis of the Stern-Gerlach experiment demonstrates a fundamental connection to relativistic quantum mechanics, revealing how nature reconciles discrete and continuous degrees of freedom within a quantum framework. Through representing a basic quantum measurement, the research establishes an operational concept for spin-1/2 particles utilising irreducible unitary representations of the Poincaré group to encode particle preparation information. Extending this, irreducible two-particle representations determine the electromagnetic interaction and yield a value for the electromagnetic coupling constant that aligns with experimental observations. Importantly, the work suggests the electromagnetic coupling constant functions as a normalisation factor for two-particle states, offering a means to address inconsistencies within the Standard Model’s perturbation algorithm.

This correction arises from recognising the incompatibility between the local structure of the interaction term and the structure of two-particle states dictated by Poincaré symmetry. Furthermore, the application of irreducible representations to N spinless particles defines a quantum gravity described by conformal gravity in the quasi-classical limit, with a galaxy-specific gravitational constant matching experimental values. The authors acknowledge that this galaxy-dependence of the gravitational constant warrants further investigation, particularly regarding its implications for cosmological models and galactic evolution. They also note that Einstein’s theory of gravity can be understood as an approximation to conformal gravity, valid for local gravitational phenomena within a galaxy.